F-numbers

The F-numbers that define aperture settings are so common that they are frequently taken for granted. But what do they mean and what is it that makes an F-number on one lens identical to the same F-number on a totally different lens?

There was a time when aperture adjustments were made by turning a collar on the lens. The user simply looked to see what F-number was needed and set that against an index mark. Today it is more common to make the same adjustments by rotating a thumbwheel on the camera body but the figures that are displayed on the LCD panel and in the viewfinder are still the same F-numbers.

F-numbers are a measure of the size of the hole through which light is collected when a picture is taken. A bigger hole, which unfortunately corresponds with a smaller F-number, gives a brighter picture. This is the same way that the human eye works when its pupil dilates to let-in more light under low levels of illumination.

So does that mean that an F-number is no more than a measure of the diameter of the hole? No, it’s not quite that simple.

Different lenses have different focal lengths, meaning that they project their images onto the sensor from different distances. If we were to imagine a camera lens as a single element then the element’s distance from the sensor would be equal to its focal length (when photographing very distant scenes). So a 200mm lens would be 200mm from the sensor, a 100mm lens would be 100mm from the sensor and so on.

Now think again about the hole through which the light travels: if the hole is farther away from the sensor then it would appear to be smaller than if it were closer. This means that the light-gathering effect of the aperture depends not just on the diameter of the hole but also on its distance from the sensor. The combination of these two factors gives the value of the F-number.

The F-number of an aperture setting is equal to the focal length of the lens divided by the diameter of the hole. This means that if a 100mm lens is set to an aperture diameter of 50mm then the F-number will be 2.

So if you are using your camera in Program mode and the metering recommends an exposure time of 1/500s with an F-number of 2, then you know that your 100mm lens will be set to an aperture diameter of 50mm. Now think about the 200mm lens, which is also going to be used at 1/500s and F2: in this case the aperture diameter must be 100mm and the front element of the lens therefore needs to be that much bigger. This comparison is illustrated in the accompanying diagram.

Modern camera lenses are more complicated than the single element that we have discussed here but the principle is the same and the massive increase in manufacturing demands that big elements introduce explains why fast-aperture (low F-number) lenses get so expensive at longer focal lengths.